Publication detail
Application of 2D PGA as an Subalgebra of CRA in Robotics
TICHÝ, R.
English title
Application of 2D PGA as an Subalgebra of CRA in Robotics
Type
conference paper
Language
en
Original abstract
We present a concept of 2D Projective Geometric Algebra (PGA) as a subalgebra of Compass Ruler Algebra (CRA) to handle problems in computer graphics and engineering efficiently in terms of an algebra with minimal dimension. In this case, we can benefit from both CRA and PGA simultaneously. When we deal with complex problems, we can use CRA objects such as circles but at the same time we can switch to PGA as a subalgebra of CRA to handle operations with flat-objects more efficiently without the change of structure of any further implementation. We demonstrate this approach on example of inverse kinematics of a planar 3-link manipulator.
English abstract
We present a concept of 2D Projective Geometric Algebra (PGA) as a subalgebra of Compass Ruler Algebra (CRA) to handle problems in computer graphics and engineering efficiently in terms of an algebra with minimal dimension. In this case, we can benefit from both CRA and PGA simultaneously. When we deal with complex problems, we can use CRA objects such as circles but at the same time we can switch to PGA as a subalgebra of CRA to handle operations with flat-objects more efficiently without the change of structure of any further implementation. We demonstrate this approach on example of inverse kinematics of a planar 3-link manipulator.
Keywords in English
Projective geometric algebra;Compass ruler algebra;Inverse kinematics
Released
18.10.2020
Publisher
Springer Science and Business Media Deutschland GmbH
Location
Switzerland
ISBN
978-3-030-61863-6
Book
Advances in Computer Graphics
Volume
2020
Number
12221
Edition number
12221
Pages from–to
472–481
Pages count
10
BIBTEX
@inproceedings{BUT170613,
author="Radek {Tichý},
title="Application of 2D PGA as an Subalgebra of CRA in Robotics",
booktitle="Advances in Computer Graphics",
year="2020",
volume="2020",
number="12221",
month="October",
pages="472--481",
publisher="Springer Science and Business Media Deutschland GmbH",
address="Switzerland",
isbn="978-3-030-61863-6"
}